- #1

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## Main Question or Discussion Point

So I've derived the equation for the amplitude of a driven oscillator as:

[itex]\huge A=\frac{F}{m\sqrt{(\omega_{0}^{2}-\omega_{d}^{2})^{2}+4\gamma^{2}\omega_{d}^{2}}}[/itex]

Which is what my lecturer has written. Then taking the derivative and setting it to 0 to get the turning point. He makes this leap:

https://imgur.com/a/gE7Y0Di

How does he do that? I can't do it.

Also an auxiliary question. I was watching Walter Lewin on this here .

And he uses

[itex]\huge

{\gamma}=\frac{b}{m}[/itex]

Whereas I've been taught:

[itex]\huge

{\gamma}=\frac{b}{2m}[/itex]

Where ϒ is the damping coefficient. Which is correct?

[itex]\huge A=\frac{F}{m\sqrt{(\omega_{0}^{2}-\omega_{d}^{2})^{2}+4\gamma^{2}\omega_{d}^{2}}}[/itex]

Which is what my lecturer has written. Then taking the derivative and setting it to 0 to get the turning point. He makes this leap:

https://imgur.com/a/gE7Y0Di

How does he do that? I can't do it.

Also an auxiliary question. I was watching Walter Lewin on this here .

And he uses

[itex]\huge

{\gamma}=\frac{b}{m}[/itex]

Whereas I've been taught:

[itex]\huge

{\gamma}=\frac{b}{2m}[/itex]

Where ϒ is the damping coefficient. Which is correct?